perplexus.info :: General : An inconsistent climber

An inconsistent climber (Posted on 2002-04-25)

A mountain climber is journeying up a mountain trail. He starts out with the sunrise, and gets to the peak just as the sun is setting. Throughout the day, he moves with inconsistent speed, slowing down to rest a few times.

He spends the night at the top, and in the morning sets out downward, reaching basecamp by nightfall. (Even though the going is easier, he stops a number of times to admire the scenery and rest.)

Is there an altitude on the mountain slope for which the climber was at that exact altitude at the same point during both days? Why or why not?

Submitted by levik

Rating: 3.3000 (10 votes)

Solution: (Hide)

Let's call our climber "Bill". Imagine a climber "John coming down the mountain in the same exact way that Bill comes down it, but a day earlier.
In other words, John is coming down the mountain on the same day as Bill is ascending it. Now with Bill going up, and John going down, the two men will be on the same altitude at some point in the day.
Because Bill going down and John going down will follow the same path, John will, at that poing, be at the same altitude as Bill will be in 24 hours. So, that is the point in time that Bill is at the same altitude on both the days.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	K Sengupta	2007-04-01 15:14:32
Comment	Old Original Oskar!	2005-02-22 11:02:28
Great Puzzle	Bruce Brantley	2004-08-22 19:46:57
kela!	rajesh	2003-07-10 20:53:01
how about this?	rajesh	2003-07-10 20:51:00
regarding my previous posting	O	2003-05-09 22:15:57
re: inconsistent climber	O	2003-05-09 22:10:56
re: inconsistent climber	Gamer	2003-03-09 14:19:36
re: inconsistent climber	Dan	2002-09-07 17:39:52
inconsistent climber	Jasper	2002-04-25 11:45:58

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